I wouldn't buy either one of those brands' earliest version of that model(70-200 f2.8) for the possibility of inconsistent AF. Both of those companies have come a long way in reverse engineering Canon's algorithms. For me, I would only be looking at their IS equivalents(VC tam/OS sig) and those put you in a very similar price point to Canon's own non-IS version of the 70-200 f2.8 or the f4IS. And if I'm sitting at similar price points I will always choose Canon first. And I would specifically buy the f4IS and keep your 100f2. It's tough when limited in funds. But I guarantee you'll get better results using your 100f2 @ f2.8 than those 1st version(cheaper non-stabilized) Tam/Sig 70-200 f2.8 wide open. I know there's not a lot of room to crop with only 12.8MP but I would even bet you could crop to the equivalent 135 FOV and still produce great results with your 5d/100f2 combo. I LOVE my 5d/135f2 combo and I feel comfortable cropping in a bit on that lens too. I can squeak out an extra bit of 'focal length' and be happy with the result.
Ever think about picking one of those up? They've come down in price. Let's throw you another curve ball...Find a 135L used for $650...
Renowned lens, getting 'cheap' these days, pairs VERY well with the original 5d and will SMOKE the other two brands early 70-200 versions in AF speed and accuracy.
OR if you just need the reach what about a used Canon 200mm f2.8 prime? You can find those between $400-550. Will be lighter/sharper/faster AF.
Lots of choices for you. My best advice is putting what you shoot in perspective. Don't get lost in the what could I do with this 'new' lens but more so, what do you see you're actually missing from what you currently have in your bag. I have swapped a LOT of gear over the last 3 years thinking I could do better with something else. Zooms are enticing for their convenience. But do not forget about their limitations. Would you be happy with the results of either of those two(your original interest) shooting wide open? IF not, they're really 'not' f2.8 for you then. My wife's setup is the 6D + tam 24-70 and we RARELY use it wide open. Only when we are already sitting at 1600. 85% of the time we're at f3.5. That's 2 stops slower than your 50 STM and almost 2 for your 100f2.
Of the Tam/Sig question....I would try to find a clean used copy of the Tamron 70-200 f2.8 VC. Now that the G2 version's been out for a few months the original one is coming down in price.
Don't buy the first version, find out it's just not that good, have to try to resell it, possibly lose money, and then save back up for what you should have purchased originally. Put all your options in a pile, read/watch reviews on all of it, then make your decision. And then come back here and show us awesome images with your 5d